Question

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of $100$private practice doctors and $150$hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table

What is the $p-$value?

Short answer

The$p-$value is$0.00051.$

Step-by-step solution

Given information

The given data is

Explanation

From the given data

$df=(no.ofcolumns-1)(no.ofrows-1)$

$$\begin{gathered} =(4-1)(2-1) \\ =3\times 1 \\ =3 \end{gathered}$$

The chi-square test statistic is

$\sum _{i,j}\frac{(O-E{)}^2}{E}$

Expected values are $E$, observed values are $O$, and the number of rows and columns in the table are $i,j$.

Using MS Office Excel, the calculated test statistic is

$x^2=22.5037$

$p-$value$$\begin{gathered} =P\left({\chi }^2>22.5037\right) \\ =0.00051 \end{gathered}$$